Pressure-driven flow in a channel with porous walls

The finite-Reynolds-number three-dimensional flow in a channel bounded by one and two parallel porous walls is studied numerically. The porous medium is modelled by spheres in a simple cubic arrangement. Detailed results on the flow structure and the hydrodynamic forces and couple acting on the sphere layer bounding the porous medium are reported and their dependence on the Reynolds number illustrated. It is shown that, at finite Reynolds numbers, a lift force acts on the spheres, which may be expected to contribute to the mobilization of bottom sediments. The results for the slip velocity at the surface of the porous layers are compared with the phenomenological Beavers-Joseph model. It is found that the values of the slip coefficient for pressure-driven and shear-driven flow are somewhat different, and also depend on the Reynolds number. A modification of the relation is suggested to deal with these features. The Appendix provides an alternative derivation of this modified relation.